New chat PYQ Library Doubts Rank report

Sign in to see Recents

Sign in to save progress →

Differentiation question

2023 · 8 Apr · Shift 1 · Q23

Guest · try one question or challengeGuest · try one question or challenge

PYQ Library
JEE Main
Mathematics
Differentiation
2023 · 8 Apr · Shift 1 · Q23

Differentiation question

2023 · 8 Apr · Shift 1 · Q23

JEE MainMathematicsDifferentiationMCQ+4 / −1

Let

f(x)=\frac{\sin x+\cos x-\sqrt{2}}{\sin x-\cos x}, x \in[0, \pi]-\left\{\frac{\pi}{4}\right\}

. Then

f\left(\frac{7 \pi}{12}\right) f^{\prime \prime}\left(\frac{7 \pi}{12}\right)

is equal to

A
$\frac{2}{3 \sqrt{3}}$
B
$\frac{2}{9}$
C
$\frac{-1}{3 \sqrt{3}}$
D
$\frac{-2}{3}$

More from Differentiation

For the differentiable function $f : R - {0} \to R$ , let $3 f (x) + 2 f (\frac{1}{x}) = \frac{1}{x} - 10$ , then $f (3) + f^{'} (\frac{1}{4})$ is equal to2023 · MCQ
Let $f (x) = \sum_{k = 1}^{10} k x^{k}, x \in R$ . If $2 f (2) + f^{'} (2) = 119 (2)^{n} + 1$ then $n$ is equal to 2023 · Numerical
If $f (x) = x^{3} - x^{2} f^{'} (1) + x f^{''} (2) - f^{'''} (3), x \in R$ , then2023 · MCQ
Let $y (x) = (1 + x) (1 + x^{2}) (1 + x^{4}) (1 + x^{8}) (1 + x^{16})$ . Then $y^{'} - y^{''}$ at $x = - 1$ is equal to2023 · MCQ
Let $f : R \to R$ be a differentiable function that satisfies the relation $f (x + y) = f (x) + f (y) - 1, \forall x, y \in R$ . If $f^{'} (0) = 2$ , then $∣ f (- 2) ∣$ is equal to .2023 · Numerical
Let $f$ and $g$ be the twice differentiable functions on $R$ such that $f^{''} (x) = g^{''} (x) + 6 x f^{'} (1) = 4 g^{'} (1) - 3 = 9 f (2) = 3 g (2) = 12$ . Then which of the following is NOT true?2023 · MCQ
Let $f^{1} (x) = \frac{3 x + 2}{2 x + 3}, x \in R - {\frac{- 3}{2}}$ For $n \geq 2$ , define $f^{n} (x) = f^{1} o f^{n - 1} (x)$ . If $f^{5} (x) = \frac{a x + b}{b x + a}, gcd (a, b) = 1$ …2023 · Numerical
Let $y = f (x) = sin^{3} (\frac{π}{3} (cos (\frac{π}{3 2} (- 4 x^{3} + 5 x^{2} + 1)^{\frac{3}{2}})))$ . Then, at x = 1,2023 · MCQ